assessment
£20-250 GBP
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Below are the quarterly returns on investment (in £000s) of two different investment projects that
had the same initial outlay. There is a sample of 16 quarters of returns and your manager has asked
you to investigate the relative performance of each project. In particular, your manager suspects
that ‘Investment B’ outperforms ‘Investment A’ and she would like you to test this hypothesis.
Perform an appropriate statistical test that incorporates your manager’s hypothesis.
Quarter Investment A Investment B
2012Q1 78 95
2012Q2 83 93
2012Q3 75 84
2012Q4 77 93
2013Q1 73 90
2013Q2 75 84
2013Q3 85 88
2013Q4 81 91
2014Q1 86 93
2014Q2 79 87
2014Q3 79 75
2014Q4 75 86
2015Q1 85 77
2015Q2 72 77
2015Q3 75 90
2015Q4 81 98
The table below represents the results from 100 different marketing campaigns performed over
three different products; the table splits between the products (Product A, B and C), and between
the success of the marketing campaign, segregating between those which demonstrate: no increase
in sales before and after the campaign; and, an increase in sales compared to before the campaign.
Your manager thinks that the success of the marketing campaigns is different across different
products, but she does not know if this result is statistically significant. Test this hypothesis with an
appropriate statistical test.
Product A Product B Product C
No increase in sales 7 10 36
Increase in sales 18 10 19
Q} The head office of a large retailer feels that one of its stores is outperforming the overall sales of
their UK shops in general. They would like to promote this fact, and further, try to learn and
understand more about their success. However, they want to know that this result is a fair
interpretation of the data, and ask you to perform a test of statistical significance on this result.
The national monthly sales for the retailer are normally distributed with a mean of £45,000 and a
standard deviation of £10,000. For the individual store in question, there are data for 12 months of
sales which has a sample mean of £47,000. Perform a statistical test on the claim that the store is
outperforming the UK average, assuming that monthly sales are normally distributed.
Q} For one of the questions above, prepare a short report on the results. Do this assuming a wide
audience with differing levels of knowledge in the area of statistics and hypothesis testing
(therefore, explain the processes involved in simple but formal language). In particular, discuss the
following:
The idea behind hypothesis testing and why this is important;
The process performed in order to get the results, the key assumptions in this process, and
the appropriateness of these assumptions to the question;
The result, how to interpret the result, and the meaning of the p‐value.
Within this, feel free to bring in other knowledge you have from the question which you did not
apply in previous questions that you feel would best describe the process and result to a wide
audience (for example, calculating other factors from the numbers and/or graphs). This is meant to
be a (very brief) report which you would happily present in a business format.
State the null and alternative hypothesis;
State the test statistic and how this statistic will be distributed if the null hypothesis is true;
Calculate the value of the test statistic;
Calculate the p‐value associated with this test statistic;
State whether the null hypothesis can be rejected at an appropriate significance level (in
order to do this, state the significance level you are applying and why).
Illustrate this in a sketch of the distribution and the resulting test statistic.
Ταυτότητα Εργασίας: #13779112
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